Let for measured in radians

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

f(x)=\sec x

for

x

measured in radians. A point

P

lies on the graph of

f

x=\dfrac{\pi}{4}

. (1) Calculate

f'(\dfrac{\pi}{4})

. Show all necessary algebraic work. (2) Write an explicit equation for the tangent line to the graph of

f

at point

P

. Express the equation in point–slope form. (3) Determine the equation of the line normal to the graph of

f

at point

P

. Express the equation in slope–intercept form.