1 Answer
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 agoRelated Questions
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