Question #1863

Find the number c that satisfies the conclusion of Rolle's Theorem.
f(x)= √(x ) - 1/3 x
[0, 9]

Expert's answer

f(0) = 0 - 1/3*0 = 0;

f(9) = 3 - 1/3*9 = 0.

Let's find the point where the first derivative is equal to zero:

f'(x) = 1/(2√x) - 1/3 = 0

3 - 2√x = 0, & x<>0

√x = 3/2;

x = 2.25.

c = 2.25

f(9) = 3 - 1/3*9 = 0.

Let's find the point where the first derivative is equal to zero:

f'(x) = 1/(2√x) - 1/3 = 0

3 - 2√x = 0, & x<>0

√x = 3/2;

x = 2.25.

c = 2.25

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