Question

The slopes of the tangents at the points where
the curve y = x2 - 4x intersects the x-axis is
​

Answer 1

Answer:

I still put out my de ye recod for the record

Answer 2

The slopes of the tangents at the points where

the curve y = x2 - 4x intersects the x-axis is  -4

​Step-by-step explanation:

Given the curve is $\textrm{y}=\textrm{x}^{2} -4\textrm{x}$

Differentiating with respect to $\textrm{x}$ we get

$\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=\frac{\mathrm{d} }{\mathrm{d} \textrm{x}}(\textrm{x}^{2}-4\textrm{x})$

or $\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=\frac{\mathrm{d} }{\mathrm{d} \textrm{x}}\textrm{x}^{2}-\frac{\mathrm{d} }{\mathrm{d} \textrm{x}}}4\textrm{x}$

or $\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=2\textrm{x}-4\times 1$

As we know $\frac{\mathrm{d} }{\mathrm{d} x}\textrm{x}^{n}=n\textrm{x}^{n-1},\textrm{ n is exponent}$

or $\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=2\textrm{x}-4$

curve intersects at x axis so x=0

so we have $\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=2\times0-4$

so $\frac{\mathrm{d}\textrm{y}}{\mathrm{d} \textrm{x}}=-4$

So slope of the tangent is -4