Question

What is the slope of the tangent to the curve y=x^2 at the point (2,4)?

Answer 1

y = x²   ⇒   dy/dx = 2x

At point (2, 4), take x = 2.

Hence slope will be 2 × 2 = 4.

Answer 2

Given,

A curve, y = x² is given.

To find,

The slope of the tangent to the curve y=x²at the point (2,4).

Solution,

The slope of the curve is generally obtained by taking the derivative of y with respect to x.

⇒   $\frac{dy}{dx}=\frac{d(x^{2}) }{dx}$

⇒   $\frac{dy}{dx}= 2$

After differentiating the equation of the curve with respect to x we have got the value of slope i.e. $\frac{dy}{dx}= 2$.

Now, it is given that we have to find the slope of the tangent to the curve y = x² at point (2,4). This means the value of x is already provided to us in the question i.e. 2. So, we can put the value of x =2 in 2x.

$\frac{dy}{dx}= 2(2)$ = 4.

Hence, the slope of the tangent to the curve y = x² at point (1,2) is 4.