The absolute extrema of a function are the largest and smallest y-values of the function on a given domain. This domain may be given to us (as in this problem) or it might be the domain of the function …

Jan 15, 2016 · To find the second derivative of the function, first simplify #f (x)#.

(dy)/ (dx)= (cos^2t-tsin2t)/ (2t-cost+tsint) To find derivative of a parmetric equation such as f (t)= (x (t),y (t)), we use formula (dy)/ (dx)= ( (dy)/ (dt))/ ( (dx ...

This means that is may be a point of inflection. We can check a graph of the function: graph {-5x^5-2x^4-2x^3+14x-17 [-2.5, 2.5, -120, 100]} Graphically, x=0 does appear to be a point of inflection (the …

Explanation: what you are looking for is the instantaneous gradient at #x=1#. To do so, you must find the derivative of the function, and substitute the #x=1# into the derivative to find the gradient.

Explanation: The concavity of a function can be determined through the second derivative; a positive value indicates it is concave at that point (curving upward), and a negative value indicates it is …

Explained below Given function f(x)= 1/x 1. This function is defined for all x on the number line, except at x=0. Hence the domain in interval form would be (-oo,0)U(0,oo) 2 &3.Vertical asymptote is x=0 or y- …

The graphs for the functions, x=-t+10, v=-1, and a=0. This is a derivatives problem, where v=(dx)/(dt) and a=(d^2x)/(dt^2). Since we are given that x(t) is negative linear, we can infer that the velocity …

The linear function y=30x+25 represents the total weight y (in pounds) of the wagon and its contents after you have loaded x blocks? What is the derivative of ln(x2 +1 2x)? What are the critical points of …

2. The derivative of a function at a certain point gives the slope of the line tangent to that point. First, we will equat #f (x)# and #y# to simply the notation.