TS EAMCET · Maths · Application of Derivatives
If the slope of the tangent of the curve \(y=a x^3+b x+4\) at \((2,14)\) is 21 , then the values of \(a\) and \(b\) respectively
- A \(2,-3\)
- B \(3,-2\)
- C \(-3,-2\)
- D 2, 3
Answer & Solution
Correct Answer
(A) \(2,-3\)
Step-by-step Solution
Detailed explanation
The curve \(y=a x^3+b x+4\) is passes through (2, 14). \[ \begin{array}{rlrlrl} & \therefore & & 14 & =a(2)^3+b(2)+4 \\ \Rightarrow & & 14 & =8 a+2 b+4 \\ \Rightarrow & & 5 & =4 a+b \end{array} \] Slope of tangent to the curve \(y=a x^3+b x+4\) i.e. \(\frac{d y}{d x}=3 a x^2+b\)…
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