Determine the gradient of the curve: y=x^2 +sin (pix/2)

Question

at the point when x= -1?

Answer 1

To find gradient of curve we must fallow these 2 steps 

[1]    Find the general gradient of the curve using dy/dx.

[2]    Substitute the x coordinate value of the given point
        into the expression found for dy/dx.

The curve y = x² + sin(πx/2).

Derivative of xⁿ = nx^{n- 1}.

Derivative of sin x = cos x.

dy/dx = 2x + (π/2)cos(πx/2)

At x = - 1,

dy/dx = 2(- 1) + (π/2)cos(π(- 1)/2)

= - 2 + (π/2)cos(- π/2)

= - 2 + (π/2)cos(π/2)

= - 2 + (π/2)(0)

= - 2.

Hence gradient of the curve at given point is - 2.