Application of Derivatives
Find the equations of all lines having slope 0 which are tangent to the curve y=x2−2x+31.
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)=−2andfprime(x)≥2 for all x∈[1,6], then find the range of values of f(6)˙
Displacement s of a particle at time t is expressed as s=21t3−6t˙ 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?