Mathematics

Problem

Let

f(x)=\sec x

for

x

measured in radians. A point

P

lies on the graph of

f

x=\dfrac{\pi}{4}

. a. Calculate

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

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

f

at point

P

. Express the equation in point–slope form. c. Determine the equation of the line normal to the graph of

f

at point

P

. Express the equation in slope–intercept form.