A continuous and differentiable function `y=f(x)` is such that its graph cuts line `y=m x+c` at `n` distinct points. Then the minimum number of points at which `f''(x)=0` is/are (a)`n-1` (b) `n-3` (c)`n-2` (d) cannot say

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

Let f: R->R be a continuous onto function satisfying f(x)+f(-x)=0AAx in R . If f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5], then the minimum number of roots of the equation f(x)=0 is

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in [0,1]for which f^(prime)(c)(f(c))^(n-1)>sqrt(2^(n-1)) , where n in Ndot

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < de, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))+1)^(n) is (a) 2n (b) 3n (c) 2n+1 (d) 3n+1

Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y/b=2 at the point (a,b), whatever be the value of n.

The graph y=2x^3-4x+2a n dy=x^3+2x-1 intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.

Draw the graph of the function y=f(x)=lim_(ntooo) cos^(2n)x and find its period.