Question

If the slope of the tangent to the curve $$y=a{ x }^{ 3 }+bx+4$$ at $$(2,14) = 21$$, then the values of $$a$$ and $$b$$ are respectively

A
2,3
B
3,2
C
3,2
D
2,3

Solution

The correct option is D $$2,-3$$$$(2,14)$$ lies on the curve $$y=ax^3+bx+4$$=> $$8a+2b+4=14$$=> $$4a+b=5$$----(1)$$\dfrac{dy}{dx}=3ax^2+b|_{x=2}=21$$=> $$12a+b=21$$--(2)Solving equations (1) and (2), we get $$a=2, b=-3$$Mathematics

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