Application of Derivatives
Prove that the curves x=y2and xy=k cut at right angles* if 8k2=1.
Let f(x0 be a non-constant thrice differentiable function defined on (−∞,∞) such that f(x)=f(6−x)andfprime(0)=0=fprime(x)2=f(5)˙ If n is the minimum number of roots of (fprime(x)2+fprime(x)fx=0 in the interval [0,6], then the value of 2n is___
Find the maximum value and the minimum value and the minimum value of 3x4−8x3+12x2−48x+25 on the interval [0,3]˙
If t is a real number satisfying the equation 2t3−9t2+30−a=0, then find the values of the parameter a for which the equation x+x1=t gives six real and distinct values of x .
Prove that the tangent drawn at any point to the curve f(x)=x5+3x3+4x+8 would make an acute angle with the x-axis.