Question

If y=4x^2 find slope of y-x curve at point p(1,4)

Answer 1

Given,

Equation of the curve y = 4x²

To Find,

The slope of the curve at (1,4)

Solution,

The slope of a curve is calculated by the dy/dx of that curve.

So, the equation of the curve is

y = 4x²

Now, differentiating this equation with respect to y.

dy/dx = 8x

Now, the slope at (1,4) will be

dy/dx = 8(1) = 8

Hence, the slope of the curve y = 4x² will be 8.

Answer 2

Answer:

We have to find the slope of the curve given as y = 4x² at a point which is given as p(1,4).

Step-by-step explanation:

Given : The equation of the curve, y = 4x².

We can identify that the equation is a parabola.

To Find: The value of the slope of the curve at the point p(1,4).

Now, prior to attending the question, we must know some important things.

What is a Slope?

Slope of any curve is defined as the angle the tangent of the same curve makes with the x - axis. In a more simplified version, a slope is the angle made by a tangent of a curve with the horizontal or x - axis.

Now, for finding the slope of a curve, we differentiate the curve.

That is, for the curve y = 4x², we have:

y = 4x²

dy/dx = 4×2x

dy/dx = 8x

Therefore, slope of the curve 4x² would be given by the formula 8x, for any point.

Now, for point p = (1,4), we have:

Slope = 8x

= 8×1                                                [the point is (1,4)]

= 8

Hence, the value of slope of the curve y = 4x² at a point p = (1,4) would be 8.