Matching functions with derivatives? Match the functions (a)–(d) in the first set of figures with the derivative functions (A)–(D) in the next set of figures. (a) (b) (c) (d) (A) (B) (C) (D)

SOLUTION To find the derivative of a line choose 2 points in the line (x y ),1, 1y ) 2nd 2ubstitute it in the y2y1 equation of the slope m = x2x1 In this question it is enough to find whether the slope is positive or negative and check which derivative graph(A-D) matches the conditions of which original graph(a-d). STEP 1 Take the graph (a) a) The derivative of the graph or the slope of the graph at all points of the function is positive. This condition is satisfied in the derivative graph D.ie for all the x-values D, Y-value is positive. STEP 2 Now take the graph (b). b) The derivative or the slope of the tangent is negative for x < 1 and x > 1 and is positive for 1 < x < 1. This condition is satisfied in the graph C,ie for x < 1 and x > 1 in C y value is negative and for 1 < x < 1, y value is positive. STEP 3 Now take the graph (c). The derivative or the slope of the tangent is negative for x < 0 and is positive for x > 0. This condition is satisfied in the graph B,ie for x < 0 in B y value is negative and for x > 0, y value is positive. STEP 4 The derivative or the slope of the tangent is negative at all points of the function. This condition is satisfied in the derivative graph A.ie for all the x-values A, Y-value is positive. 1