Provide an appropriate response.
-Suppose that f'(x) = 2x for all x. Find f(7) if f(-2) = 2.
A) 49
B) 51
C) 45
D) 47

Question

Quizplus · Accepted Answer

Using the information given in the problem, we can integrate f'(x) to find f(x):
f'(x) = 2x
∫f'(x) dx = ∫2x dx
f(x) = x^2 + C, where C is a constant of integration
To find C, we use the fact that f(-2) = 2:
f(-2) = (-2)^2 + C = 2
C = 2 - 4 = -2
So we have:
f(x) = x^2 - 2
To find f(7), we substitute x = 7 into the equation for f(x):
f(7) = 7^2 - 2 = 49 - 2 = 47, so the answer is D.

Provide an Appropriate Response