Let f(x) be a function defined in an open interval containing 'a'. The derivatrive of th on f(x) at 'a', denoted by f'(a) is defined by f'(a) = lim f(ath)-f(a) h→0 h. Provided this limit exists. This is also called Slope (m) of the tangent of function at point (a, f(a)) Example 1. Find the derivative of the following functions at the indicated points. Or Find the Slope of the following functions at the given points. f(x) = x3 7x +3 at x = 1 Solution:

Q: Sketch a graph of a function ƒ with the following propertie. ƒ' < 0 and ƒ" < 0, for x < 3ƒ'…

A: Since f’ < 0, this means the function is decreasing for all values of x. Since f’’ < 0 for x…

Q: Consider the function f(x) = x^3 - 4x^2 + 5x - 2. Determine the points on the graph of f(x) at…

A: The tangent line to a graph of a function at a specific point is a line that just touches the graph…

Q: The graph Figure 6 is the derivative of a function f which is defined only for 0 < x < c. f b Figure…

A:

Q: use tangent lines to find a b c using f(x)= ax^3+bx+c with intersections at -2,-2 and 1,1 with a y…

A:

Q: Sketch the graph of a function continuous on the given interval that satisfies the following…

A: Given, f is continuous on -∞,∞; f'(x)&lt;0 and f''(x)&lt;0 on -∞,0; f'(x)&gt;0 and f''(x)&gt;0 on…