Let f ( x ) = x 3/5 for x ≤ 1 , and f ( x ) = − ( x − 2 ) 3 for x > 1 . How many critical points does its graph have?

Start Free Mock LoginAlready registered? Login here

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumsingle choice

Let $f (x) = x^{3/5}$ for $x \leq 1$ , and $f (x) = - (x - 2)^{3}$ for $x > 1$ . How many critical points does its graph have?

Options:

Answer:

Solution:

At $x = 0, f'$ does not exist; at $x = 1$ , the two formulas join but the one-sided derivatives differ; and at $x = 2, f' = 0$ . Hence there are three critical points: $0, 1, 2$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...