Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and

Question

2 years ago

10

c?

1 answer:

galina1969 [7] · Answer 1 · 2023-06-08T18:17:59+03:00

The values of b and c are -4 and 4 respectively

<h3>How to determine the values of b and c?</h3>

The function is given as:

f(x) = x^2 + bx + c

Differentiate f(x)

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for b

b = -2x

The minimum is (2, 0).

So, we have:

b = -2 * 2

b = -4

Substitute b = -4 in f(x) = x^2 + bx + c

f(x) = x^2 - 4x + c

Substitute (2, 0)

0 = (2)^2 - 4(2) + c

This gives

0 = 4 - 8 + c

Evaluate

c = 4

Hence, the values of b and c are -4 and 4 respectively