Chapter 4: Q. 3 (page 364)

Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = 3 e^{2 x} + 1, f (0) = 2$

Short Answer

Expert verified

$Hence the function is 3 e^{2 x} \times 2 + x - 4$

The value of f(-4) = $3 \times e^{- 8} - 8$

Step by step solution

Step 1. Given

The given function is $f' (x) = 3 e^{2 x} + 1, f (0) = 2$

Step 2. Finding the function using integration

$Integrating function with respect to x \int f' (x) = \int 3 e^{2 x} + 1, f (0) = 2 = \int 3 e^{2 x} + 1 d x = 3 e^{2 x} \times 2 + x + c where c is constant when f (0) = 2 f (0) = 3 e^{2 * 0} * 2 + 0 + c 2 = 6 + c c = - 4 Hence the function is 3 e^{2 x} \times 2 + x - 4$

Step 3. Finding the value f(c)

$f (x) = 3 e^{2 x} \times 2 + x - 4 f (- 4) = 3 \times e^{2 * - 4} + (- 4) - 4 = 3 \times e^{- 8} - 8$

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Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = 3 e^{2 x} + 1, f (0) = 2$

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding the function using integration

Step 3. Finding the value f(c)

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Find a function f that has the given derivative f' and value f(c), if possible. f'(x)=3e2x+1,f(0)=2

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding the function using integration

Step 3. Finding the value f(c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = 3 e^{2 x} + 1, f (0) = 2$