If y = 7x – x3 and x increases at the rate of 4 units per second, how fast is the slope of the curve changing when x = 2?

Asked by Aaryan | 1 year ago |  111

##### Solution :-

Given equation of curve y = 7x – x3 and x increases at the rate of 4 units per second.

To find how fast is the slope of the curve changing when x = 2

Equation of curve is y = 7x – x3

Differentiating the above equation with respect to x, we get slope of the curve

$$\dfrac{dy}{dx}=\dfrac{d(7x-x^3)}{dx}$$

Suppose m be the slope of the given curve then the above equation becomes,

m = 7 - 3x2 ...(ii)

Given x increases at the rate of 4 units per second, therefore

$$\dfrac{dx}{dt}$$ = 4 units/sec ...(iii)

Differentiate the equation of slope that is equation (ii)

When x = 2, equation (iv) becomes

$$\dfrac{dm}{dt}$$ = (-6x) x (4)

= -6 x 2 x 4 = - 48

The slope cannot be negative,

Thus, the slope of the curve is changing at the rate of 48 units/sec when x = 2

Answered by Sakshi | 1 year ago

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