Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let f be a function such that f(2)=3 and f^(')(2)=-1. Let g be the function g(x)=x^(2). Let G be a function defined as G(x)=f(x)*g(x). G^(')(2)=

- Let f f be a function such that f(2)=3 f(2)=3 and f′(2)=−1 f^{\prime}(2)=-1 .\newline- Let g g be the function g(x)=x2 g(x)=x^{2} .\newlineLet G G be a function defined as G(x)=f(x)⋅g(x) G(x)=f(x) \cdot g(x) .\newlineG′(2)= G^{\prime}(2)=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate exponential functionsright chevron icon

Full solution

Q. - Let f f be a function such that f(2)=3 f(2)=3 and f′(2)=−1 f^{\prime}(2)=-1 .\newline- Let g g be the function g(x)=x2 g(x)=x^{2} .\newlineLet G G be a function defined as G(x)=f(x)⋅g(x) G(x)=f(x) \cdot g(x) .\newlineG′(2)= G^{\prime}(2)=
  1. Identify Product Rule: G(x)=f(x)⋅g(x)G(x) = f(x) \cdot g(x), so we need to use the product rule to find G′(x)G'(x). The product rule is (f⋅g)′=f′⋅g+f⋅g′(f \cdot g)' = f' \cdot g + f \cdot g'.
  2. Find g′(x)g'(x): First, find g′(x)g'(x) since g(x)=x2g(x) = x^2.\newlineg′(x)=2xg'(x) = 2x.
  3. Evaluate g′(2)g'(2): Now, evaluate g′(2)g'(2) by substituting xx with 22.\newlineg′(2)=2×2=4g'(2) = 2 \times 2 = 4.
  4. Determine f(2)f(2) and f′(2)f'(2): We already know f(2)=3f(2) = 3 and f′(2)=−1f'(2) = -1 from the problem statement.
  5. Apply Product Rule Formula: Now, apply the product rule: G′(x)=f′(x)⋅g(x)+f(x)⋅g′(x)G'(x) = f'(x) \cdot g(x) + f(x) \cdot g'(x).
  6. Substitute xx with 22: Substitute xx with 22 to find G′(2)G'(2): G′(2)=f′(2)⋅g(2)+f(2)⋅g′(2)G'(2) = f'(2) \cdot g(2) + f(2) \cdot g'(2).
  7. Calculate G′(2)G'(2): Calculate G′(2)G'(2) using the known values: G′(2)=(−1)×(22)+3×4G'(2) = (-1) \times (2^2) + 3 \times 4.
  8. Simplify Expression: Simplify the expression: G′(2)=(−1)×4+3×4G'(2) = (-1) \times 4 + 3 \times 4.
  9. Final Result: G′(2)=−4+12G'(2) = -4 + 12.
  10. Final Result: G′(2)=−4+12G'(2) = -4 + 12. G′(2)=8G'(2) = 8.

More problems from Evaluate exponential functions

Question
A 13 km 13 \mathrm{~km} stretch of road needs repairs. Workers can repair 312 km 3 \frac{1}{2} \mathrm{~km} of road per week.\newlineHow many weeks will it take to repair this stretch of road?\newlineweeks
Get tutor helpright-arrow

Posted 3 months ago

Question
Liam opened a savings account and deposited $6000 \$ 6000 . The account earns 5% 5 \% in interest annually. He makes no further deposits and does not withdraw any money. In t t years, he has $8865 \$ 8865 in this account.\newlineWrite an equation in terms of t t that models the situation.
Get tutor helpright-arrow

Posted 3 months ago

Question
Samantha opened a savings account and deposited $8192 \$ 8192 . The account earns 10% 10 \% in interest annually. She makes no further deposits and does not withdraw any money. In t t years, she has $25,710 \$ 25,710 in this account.\newlineWrite an equation in terms of t t that models the situation.
Get tutor helpright-arrow

Posted 3 months ago

Question
The graph of a sinusoidal function intersects its midline at (0,−7) (0,-7) and then has a minimum point at (π4,−9) \left(\frac{\pi}{4},-9\right) .\newlineWrite the formula of the function, where x x is entered in radians.\newlinef(x)= f(x)=
Get tutor helpright-arrow

Posted 3 months ago

Question
The following formula is used in economics to find a company's gross profit rate P P , where S S is the net sales and C C is the cost of goods sold.\newlineP=S−CS P=\frac{S-C}{S} \newlineRearrange the formula to highlight the cost of goods sold.\newlineC=□ C=\square
Get tutor helpright-arrow

Posted 3 months ago

Question
3⋅50.2w=720 3 \cdot 5^{0.2 w}=720 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinew≈ w \approx
Get tutor helpright-arrow

Posted 3 months ago

Question
18⋅25t=261 18 \cdot 2^{5 t}=261 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinet≈ t \approx
Get tutor helpright-arrow

Posted 3 months ago

Question
−4⋅36w=−1750 -4 \cdot 3^{6 w}=-1750 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinew≈ w \approx
Get tutor helpright-arrow

Posted 3 months ago

Question
20⋅73y=5 20 \cdot 7^{3 y}=5 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newliney≈ y \approx
Get tutor helpright-arrow

Posted 3 months ago

Question
10⋅35t4=800 10 \cdot 3^{\frac{5 t}{4}}=800 \newlineWhat is the solution of the equation?\newlineRound your answer, if necessary, to the nearest thousandth.\newlinet≈ t \approx
Get tutor helpright-arrow

Posted 3 months ago

View all (44)