Question

if f(x)=4x^2 then value of c in (-1,3)for which f(3)-f(-1)/4 =f dash (c)​

Answer 1

Answer:

c = 1

Step-by-step explanation:

f(x) = 4x²

f'(x) = 8x

f'(c) = 8c

f(3) = 4(9) = 36

f(-1) = 4

[f(3) - f(-1)]/4 = (36 - 4)/4 = 8

8 = f'(c)

8c = 8

c = 1

Answer 2

The value of c is 1.

If f(x) = 4x² , then the value of c in (-1, 3) for which

$\frac{f(3)-f(-1)}{4}=f'(c)$

here, f(x) = 4x²

at x = -1,

f(-1) = 4 × (-1)² = 4 × 1 = 4 ...(1)

at x = 3,

f(3) = 4 × 3² = 4 × 9 = 36 ...(2)

differentiating f(x) with respect to x, we get

f'(x) = 4 × 2 x²¯¹ = 8x

∴ f'(c) = 8c ...(3)

from equations (1) , (2) and (3)

$\frac{f(3)-f(-1)}{4}=f'(c)\\\\\implies\frac{36-4}{4}=8c\\\\\implies c=1$

Therefore the value of c is 1.