Question

For the curve y = (2x + 1)^3 find the rate of change of slope at x = 1

Answer 1

slope = dy/dx = 3 ( 2x + 1 )2

rate  of  change  of  slope = 6( 2x + 1 ) = 6* 3 = 18  at  x = 1

Answer = 18

Answer 2

The rate of change of slope at x = 1 for the curve is 54

Step-by-step explanation:

Given: $y = (2x+1)^{2}$ is the given equation

To find : The rate of change of slope at x = 1

Formula used : $(\frac{d}{dx} )(x^{n} ) = nx^{n-1}$

solution,

The equation of the curve

$y = (2x+1)^{2}$

Differentiate the above equation with respect to x

The we get,

$y^{'} = 3(2x +1)^{2} .2$

$y^{'} = 6(2x +1)^{2}$

Rate of change of slop at x = 1

Now sub the value of x = 1  in the above equation

$y^{'} = 6(2x +1)^{2}$

$y^{'} = 6(2(1) +1)^{2}$

$y^{'} = 6(2 +1)^{2}$

$y^{'} = 6(3)^{2}$

$y^{'} = 6(9)$

$y^{'} = 54$

Final answer:

The rate of change of slope for the curve is 54.

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