AP EAMCET · Maths · Application of Derivatives
If \(\mathrm{A}=\left\{\mathrm{x} / 9 \mathrm{x} \geq \mathrm{x}^2+20\right\}\) and \(\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}\) is defined by \(f(x)=2 x^3-15 x^2+36 x-48\), then the maximum value of \(f(x)\) is
- A -20
- B 7
- C 20
- D -16
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Given } \mathrm{A}=\left\{x: 9 \mathrm{x} \geq \mathrm{x}^2+20\right\} \\ & \mathrm{A}=\{x: x \in[4,5]\}=[4,5] \\ & \text { Given } f(x)=2 x^3-15 x^2+36 x-48 \\ & f^{\prime}(x)=6\left(x^2-5 x+6\right)=6(x-3)(x-2) \end{aligned} \] For maxima or minima…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The area of the triangle formed by the tangent to the curve \(x y=\mathrm{a}^2\) at \(\left(x_1, y_1\right)\) on it and the axes isAP EAMCET 2022 Medium
- If a variable straight line passing through the point of intersection of the lines \(x-2 y+3=0\) and \(2 x-y-1=0\) intersects the \(\mathrm{X}, \mathrm{Y}\)-axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio \(-2: 3\) isAP EAMCET 2024 Medium
- The locus of the centre of the circle, which cuts the circle \(x^2+y^2-20 x+4=0\) orthogonally and touches the line \(x=2\), isAP EAMCET 2014 Medium
- The set of all real values of \(c\) for which equation \(z \bar{z}+(4-3 i) \bar{z}+(4+3 i) z+c=0\) represents a circle isAP EAMCET 2024 Medium
- The equation of the circle which cuts the circles \(x^2+y^2+4 x-7=0\), \(2 x^2+2 y^2+3 x+5 y-9=0, x^2+y^2+y=0\) orthogonally isAP EAMCET 2019 Medium
- In \(\triangle A B C\), if \(A, B, C\) are in arithmetic progression, \(\Delta=\frac{\sqrt{3}}{2}\) and \(r_1 r_2=r_3 r\), then \(R=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- Let \(A=\{-4,-2,-1,0,3,5\}\) and \(f: \mathrm{A} \rightarrow \mathbf{R}\) be defined by \(f(x)=\left\{\begin{array}{ccc}3 x-1 & \text { for } & x>3 \\ x^2+1 & \text { for } & -3 \leq x \leq 3 \\ 2 x-3 & \text { for } & x < -3\end{array}\right.\) Then the range of \(f\) isAP EAMCET 2017 Easy
- Bag \(A\) contains 6 Green and 8 Red balls and bag \(B\) contains 9 Green and 5 Red balls. A card is drawn at random from a well shuffled pack of 52 playing cards. If it is a spade, two balls are drawn at random from bag \(A\), otherwise two balls are drawn at random from bag \(B\). If the two balls drawn are found to be of the same colour, then the probability that they are drawn from bag \(A\) isAP EAMCET 2019 Medium
- Identify the statement which is not correct?AP EAMCET 2017 Medium
- In a plane electromagnetic wave, the maximum value of the electric field component is \(4.4 \mathrm{Vm}^{-1}\). The intensity of the wave is nearlyAP EAMCET 2022 Medium
- Which of the following equations gives a circle?AP EAMCET 2005 Medium
- A stone is dropped from the top of a tall building and after 2 seconds another stone is thrown vertically downwards with a velocity \(5 \mathrm{~ms}^{-1}\) from the same point. Then the distance from the top of the building at which second stone overtakes the first is ____ \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2017 Medium