Derivatives Problems

Question

Suppose that f(x)=Msinx+NcosX for some constants M and N. If (pi/4)=3 and f'(pi/4)=1, find an equation for the tangent line to y=f(x) at the point where x=3pi/4

Answer 1

The sin and cos of π/4 both = (1/2)√2.

f'(x) = M cos x - N sin x

3= (1/2)√2(M + N)

1 = (1/2)√2(M-N)

4 = M√2 => M = 2√2

2 = N√2 = N = √2

You now have an expression for f'(x). Note that the sin 3π/4 = (1/2)√2 and cos 3π/4 = -(1/2)√2; therefore you can now evaluate f'(3π/4). Have at it!