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ELEN [110]
3 years ago
5

Let f(x) = x^2 + 6x.

Mathematics
1 answer:
rusak2 [61]3 years ago
4 0

Answer:

(A) The slope of secant line is 18.

(B) The slope of secant line is h+16.

Step-by-step explanation:

(A)

The given function is

f(x)=x^2+6x

At x=3,

f(3)=(3)^2+6(3)=27

At x=9,

f(9)=(9)^2+6(9)=135

The secant line joining (3,27) and (9,135). So, the slope of secant line is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{135-27}{9-3}=18

The slope of secant line is 18.

(B)

The given function is

f(x)=x^2+6x

At x=5,

f(5)=(5)^2+6(5)=55

At x=5+h,

f(5+h)=(5+h)^2+6(5+h)=h^2 + 16 h + 55

The secant line joining (5,55) and (5+h,h^2 + 16 h + 55). So, the slope of secant line is

m=\dfrac{h^2 + 16 h + 55-55}{5+h-5}

m=\dfrac{h^2 + 16 h }{h}

m=h+16

The slope of secant line is h+16.

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Step-by-step explanation:

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