Question

The graphs of the linear functions f and g are shown above. If h(x)=f(x)+g(x), then h′(x)=

Answer 1

Based on the graph,

     f(x) = 1/2x+3

    g(x) = -x+4

so, h(x) = -1/2 x +7

Since h'(x) is the derivative or slope of h(x) and h is a line,

h'(x) = -1/2, Answer C.

Answer 2

The required value for h'(x) is -0.5

The standard form of the equation of a line is expressed as;

y = mx+ b where:

• m is the slope

• b is the y-intercept:

From the graph shown:

f(x) = 0.5x+3  

 g(x) = -x+4

Taking the sum:

h(x) = f(x) + g(x)

h(x) = 0.5x + 3 - x + 4

h(x) = -0.5x + 7

Find the derivative:

h'(x) = -0.5

hence the required value for h'(x) is -0.5

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