Mathematics

Problem

Let

H(x)=x^{4}-4x^{2}+3\sin x-2\cos x

. a. (i) Find

H'(x)

. b. (ii) Calculate the slope of the tangent to the curve

y=H(x)

x=\dfrac{\pi}{4}

. c. (iii) Obtain the equations of the tangent and the normal to the curve at the point corresponding to

x=\dfrac{\pi}{4}