Find the equations of the two tangent lines to the graph of f that pass through

Question

Find the equations of the two tangent lines to the graph of f that pass through the indicated point. f(x)=6x-x^2 line with positive slope, line with negative slope, The tangent line to the graph of y = g(x) at the point (7, 4) passes through the point (1, 5). Find g(7) and g?(7). Find an equation of the line that is tangent to the graph of f and parallel to the given line. Find an equation of a line that is tangent to the graph of f and parallel to the given line. Consider the following function. f(x)=root x+4; (12,4) (a) Find an equation of the tangent line to the graph of fat the given point. Consider the following function. Root x, (1, 1) (a) Find an equation of the tangent line to the graph of fat the given point.

Explanation / Answer

8) Equation of tangent

y = 1/2 (x-1) +1

Y=1/2*x +1/2 (ans)

9) Y = 1/8(x-12) +4

Y = 1/8*x +5/2 (ans)

10) slope =4x =6

x =1.5 & y=4.5

Y = 4.5 + 6(x-1.5)

Y = 6x - 4.5 (ans)

11) 3x^2 =3

x= +1 ,-1

Points are (1,1)& (-1,-1)

Y = 3x -2

Y = 3x +4

So smaller intercept = -2 (ans)

Larger intercept = 4 (ans)

12) g(7) =4 (ans)

g'(7) = -1/6 (ans)

13 )Line with positive slope

Slope = 2

For negative slope =-2

Equation for positve slope

Y = 2x + 4 (ans)

Equation for negative slope

Y = -2x +16 (ans)

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