Question

For the function f ( x ) = 3 ( x + 2 ) 2 and the point P given by x = − 3 answer each of the following questions. For the points Q given by the following values of x compute (accurate to at least 8 decimal places) the slope, m P Q , of the secant line through points P and Q . -3.5 -3.1 -3.01 -3.001 -3.0001 -2.5 -2.9 -2.99 -2.999 -2.9999 Use the information from (a) to estimate the slope of the tangent line to f ( x ) at x = − 3 and write down the equation of the tangent line. Solution

Answer 1

For the function g ( x ) = √ 4 x + 8 and the point P given by x = 2 answer each of the following questions. For the points Q given by the following values of x compute (accurate to at least 8 decimal places) the slope, m P Q , of the secant line through points P and Q .

Answer 2

What we need to first is set up the formula for the slope of the secant lines
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Then we construct a table of the value of mPQ for the given values of x
picture 2 labels this
(b) the slope of the secant line is 0.5 from both sides of x=2, so the equation would be
m=0.5=1/2
now that we know the equation of the tangent line, we can set up the eqaution
the equation is: y=g(2)+m(x-2)=4+1/2(x-2) , which simplifies to y=1/2x+3
the graph is in the third picture




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Answer 3

Thanks man