AP EAMCET · Maths · Application of Derivatives
The curve \(y=a x^3+b x^2+c x+5\) touches the \(X\)-axis at \(P(-2,0)\) and cuts \(Y\)-axis at a point \(Q\), where gradient is 3 . Then the values of \(a, b, c\) are
- A \(a=\frac{-1}{2}, b=\frac{-3}{4}, c=3\)
- B \(a=\frac{1}{2}, b=\frac{3}{4}, c=3\)
- C \(a=1, b=2, c=3\)
- D \(a=-1, b=-2, c=3\)
Answer & Solution
Correct Answer
(A) \(a=\frac{-1}{2}, b=\frac{-3}{4}, c=3\)
Step-by-step Solution
Detailed explanation
The equation of given curve is \(y=a x^3+b x^2+c x+5\) ...(i) \(\because\) Curve (i) passes through point \(P(-2,0)\), so \(-8 a+4 b-2 c+5=0\) ...(ii) and curve (i) cuts the \(Y\)-axis at a point \(Q\) with gradient 3, so \(\left.\frac{d y}{d x}\right|_Q=3\)…
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