Question

Find the slope of tangent to the curve y=5x^2 at (-1;5)

Answer 1

Answer:

here is the solution !!!

Answer 2

The slope of tangent is -10.

Given:

• A curve $y = 5 {x}^{2}$
• A point (-1,5).

To find:

• Find the slope of tangent to the curve y=5x² at (-1,5)

Solution:

Formula/Concept to be used:

• Slope of tangent is given by dy/dx.
• Put the point in dy/dx to find slope at that point.

Step 1:

Find dy/dx.

$y = 5 {x}^{2}$

So,

$\frac{dy}{dx} = 5 \times 2x$

or

$\bf \frac{dy}{dx} = 10x$

Step 2:

Find slope at point (-1,5).

It is clear that x= -1 and y= 5.

$\frac{dy}{dx} \bigg |_{( - 1,5)} = 10( - 1)$

or

$\bf \red{\frac{dy}{dx} \bigg |_{( - 1,5)} = - 10}$

Thus,

The slope of tangent is -10.

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