Question

For x = 4 the function f(x) = x^2 + bx + c has the minimum value of -9. Find C.​

Answer 1

Answer:

7

Explanation:

For x=4, the function f(x) =x^2 + bx + c has the minimum value of -9. What is c?

f(x)=x2+bx+c has a minimum at x=4

Which means that its derivative at x=4,f′(4)=0

f′(x)=2x+b (Using power rule)

f′(4)=8+b=0→b=−8

Since the minimum value of f(x) is −9 at x=4

This means that f(4)=−9

16+4b+c=−9

16−32+c=−9(b=−8)

c=7