Calculus

Derivatives

Graphical Interpretation of Derivatives

         

The above graph represents the function y=g(x).y=g(x). Judging the graph as well as you can by eye, what can we say about the derivatives of g(x)g(x) at x=2,0,2?x=-2,0,2?

If the graph of y=f(x)y=f(x) is as shown above, on which of the following intervals is the slope of the tangent line always positive?

Which of the following is a possible value for the slope of the tangent line to the above curve at point P=(1,2)?P=(1, 2) ?

If the equation of the tangent line at point QQ is y=0.924x+6,y=0.924x+6, which of the following is a possible value for the slope of the tangent line at P?P ?

The above diagram is the graph of a function ff satisfying f(x)=f(x)f(-x) = -f(x). If the slope of the tangent line at point OO is 1.5421.542 and the slope of the tangent line at point QQ is 1.316,-1.316, what is the slope of the tangent line at point P?P ?

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