Class 12

Math

Calculus

Application of Derivatives

Find the equations of all lines having slope 0 which are tangent to the curve $y=x_{2}−2x+31 $.

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Find the minimum value of $(x_{1}−x_{2})_{2}+(20x_{1} −(17−x_{2})(x_{2}−13) )_{2}$ where $x_{1}∈R_{+},x_{2}∈(13,17)$.

If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is $3π ˙$

Let $g(x)=(f(x))_{3}−3(f(x))_{2}+4f(x)+5x+3sinx+4cosx∀x∈R˙$ Then prove that $g$ is increasing whenever is increasing.

Let $f$ be differentiable for all $x,$ If $f(1)=−2andf_{prime}(x)≥2$ for all $x∈[1,6],$ then find the range of values of $f(6)˙$

Find the minimum length of radius vector of the curve $x_{2}a_{2} +y_{2}b_{2} =1$

Displacement $s$ of a particle at time $t$ is expressed as $s=21 t_{3}−6t˙$ Find the acceleration at the time when the velocity vanishes (i.e., velocity tends to zero).

The two equal sides of an isosceles triangle with fixed base $b$ are decreasing at the rate of $3cm/s˙$ How fast is the area decreasing when the two equal sides are equal to the base?

Prove that there exist exactly two non-similar isosceles triangles $ABC$ such that $tanA+tanB+tanC=100.$