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

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 n-1 (b) n-3 (c) n-2 (d) cannot say

If f(x) is continuous and differerntiable function such that f((1)/(n))=0 for all n in N , then

If function y=f(x) has only two points of discontinuity say x_1,x_2, where x_1,x_2<0, then the number of points of discontinuity of y=f(-|x+1|) is (a) 0 (b) 2 (c) 6 (d) 4

Find the conditions that the straight lines y=m_1x+c_1, y=m_2x+c_2a n d\ y=m_3x+c_3 may meet in a point.

If f(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if (f(x))^(2)=1, forall x in [0,n], then number of functions f(x) are

Question 1 and 2 refer to the information and graph below. Let function f be defined by the graph in the accompanying figure. Q. Let m represents the number of points at which the graphs of y=f(x) and g(x)=3 intersect. Let n represents the number of points at which the graphs of y=f(x)-1 and g(x)=3 intersect. What is the value of m+n?

Prove that (x/a)^n+(y/b)^n=2 touches the straight line x/a+y/b=2 for all n in N , at the point (a ,\ b) .

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.

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.

A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It its graph passes through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is 1 (b) -1 (c) 2 (d) 0