Question
Asked Oct 16, 2019
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1
Find the value or values of c that satisfy the equation
f(b)f(a)
=f(c) in the conclusion of the Mean Value
b-a
Theorem for the following function and interval
f(x) 5x2x-3
-1,3
f(b)-f(a)
=f'(c) is/are
The value(s) of c that satisfy the equation
b-a
(Type a simplified fraction. Use a comma to separate answers as needed.)
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1 Find the value or values of c that satisfy the equation f(b)f(a) =f(c) in the conclusion of the Mean Value b-a Theorem for the following function and interval f(x) 5x2x-3 -1,3 f(b)-f(a) =f'(c) is/are The value(s) of c that satisfy the equation b-a (Type a simplified fraction. Use a comma to separate answers as needed.)

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Expert Answer

Step 1

Given,

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f(x) 5x22x 3 and [-1,3]

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Step 2

Here, a = -1 and b = 3

Now,

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f(a) f(-1)= 5(-1) 2(-1) 3 5 2 3 0 2(3) - 3 = 45 + 6 - 3 = 48 f (b) f(3) 5(3)2 d(f (x)) d(5x2+2x-3) And f'(x) = 10x2 11 dx dx So, f'(c) 10c2

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Step 3

Now, applying the Mean...

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f (b)-f(a) f'(c) b-a 48-0 = 10c 2 3-(-1) 10c 2 12 c = 1

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Math

Calculus

Derivative