Suppose `f(x)=x^(2)-3x+1`.If `c_(1) and c_(2)` are the two values of c for which the tangent line to the graph of f(x) at the point (c,f(c)) intersects at the point (-3,0) then `(c_(1)+c_(2))` equals

Let f(x)=x^(2)-3x+1 if c_(1) and c_(2) are two values of c for which tangent line to graph of f(x) at point (c,f(c)) intersects x axis at (3,0) then (c_(1)+c_(2)) is

If f(x)=ax^2-3x+c where f(2)=3 and f(3) =10, then: (a,c)-=

The line joining the points (0,3) and (5,-2) becomes tangent to the curve y=c/(x+1) then c=

If the tangent to the curve y= e^x at a point (c, e^c) and the normal to the parabola, y^2 = 4x at the point (1,2) intersect at the same point on the x-axis then the value of c is ____________.

If the tangent to the curve , y =f (x)= x log_(e)x, ( x gt 0) at a point (c, f(c)) is parallel to the line - segment joining the point (1,0) and (e,e) then c is equal to :

Let f be continuous on [a, b] and assume the second derivative f" exists on (a, b). Suppose that the graph of f and the line segment joining the point (a,f(a)) and (b,f(b)) intersect at a point (x_0,f(x_0)) where a < x_0 < b. Show that there exists a point c in(a,b) such that f"(c)=0.

Find value of c such that line joining the points (0, 3) and (5, -2) is a tangent to curve y=c/(x+1)

Let f (x) = x^(2) -2. If int _(3) ^(6) f (x)dx =3f (c ) for some c in (3,6) then the value of c is equal to

If f(x)=x^(2)-6x+8 and there exists a point c in the interval [2,4] such that f'(c)=0 , then what is the value of c?

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is