# Application of Derivatives · Mathematics · AP EAPCET

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AP EAPCET 2021 - 20th August Morning Shift
If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are
AP EAPCET 2021 - 20th August Morning Shift
Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are the points of maximum and minim...
AP EAPCET 2021 - 20th August Morning Shift
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.
AP EAPCET 2021 - 20th August Morning Shift
The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and 20 cm respectively. If its diameter is increasing...
AP EAPCET 2021 - 19th August Evening Shift
Given, $$f(x)=x^3-4x$$, if x changes from 2 to 1.99, then the approximate change in the value of $$f(x)$$ is
AP EAPCET 2021 - 19th August Evening Shift
If the curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect at right angles, then $$a^2$$ is equal to
AP EAPCET 2021 - 19th August Evening Shift
Let $$x$$ and $$y$$ be the sides of two squares such that, $$y=x-x^2$$. The rate of change of area of the second square with respect to area of the fi...
AP EAPCET 2021 - 19th August Evening Shift
If $$f^{\prime \prime}(x)$$ is a positive function for all $$x \in R, f^{\prime}(3)=0$$ and $$g(x)=f\left(\tan ^2(x)-2 \tan (x)+4\right)$$ for $$0 ... AP EAPCET 2021 - 19th August Morning Shift The line which is parallel to X-axis and crosses the curve$$y=\sqrt x$$at an angle of 45$$\Upsilon$$is AP EAPCET 2021 - 19th August Morning Shift If the error committed in measuring the radius of a circle is 0.05%, then the corresponding error in calculating its area would be AP EAPCET 2021 - 19th August Morning Shift The stationary points of the curve$$y=8 x^2-x^4-4$$are AP EAPCET 2021 - 19th August Morning Shift The distance between the origin and the normal to the curve$$y=e^{2 x}+x^2$$drawn at$$x=0 is units
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