Question

The angle that the tangent to the curve y=x^2 at (0,0) makes with the positive direction of the x-axis is

Answer 1

y = x²,
Slope of tangent = dy/dx
so, differentiate with respect to x
dy/dx = 2x
slope of curve at (0,0) = $\frac{dy}{dx}_{x=0,y=0}$ = 2 × 0 = 0
so, slope of tangent of curve = 0 { parallel to x axis }
hence, angle make with positive direction of x -axis by tangent is zero.

Answer 2

Solution -
            Derivative of function at any point gives slope of tangent at that point.