Consider the function

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

f(x)=3\sin x-4\cos x

. (i) Find

f'(x)

. (ii) Calculate

f'\!\left(\dfrac{\pi}{4}\right)

, giving your answer in simplest form. (iii) Determine all values of

x

in the interval

[0,2\pi]

for which

f'(x)=0

Related theory

Trigonometric Equations
Trigonometric Functions
Differentiation Rules
Derivatives of standard functions via chain rule
Exponential and logarithmic functions
Continuity and Differentiability

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