Application of Derivatives
Find the maximum and minimum values of f , if any, of the function given by f(x)=∣x∣,x∈R.
If a,b are two real numbers with a<b , then a real number c can be found between aandb such that the value of
Let f(x)andg(x) be differentiable functions such that fprime(x)g(x)=f(x)gprime(x) for any real x˙ Show that between any two real solution of f(x)=0, there is at least one real solution of g(x)=0.
Let P(x) be a polynomial with real coefficients, Let a,b∈R,a<b, be two consecutive roots of P(x) . Show that there exists c such that a≤c≤bandPprime(c)+100P(c)=0.
If the equation of the tangent to the curve y2=ax3+b at point (2,3)isy=4x−5 , then find the values of aandb .