What is the equation of the tangent line of f(x)=x^2 + sinx at x=pi?

1 Answer
Dec 3, 2015

y=(2pi-1)x-pi^2+pi

Explanation:

Find f'(pi) at the point (pi,pi^2).

f'(x)=2x+cosx

f'(pi)=2pi+cospi

f'(pi)=2pi-1

Thus, 2pi-1 is the slope of the tangent line at the point (pi,pi^2).

Write the equation of the line in point-slope form:

y-pi^2=(2pi-1)(x-pi)

In slope-intercept form: y=(2pi-1)x-pi^2+pi