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PtichkaEL [24]
3 years ago
9

Equation of the tangent line

Mathematics
1 answer:
GalinKa [24]3 years ago
5 0
Find the eqn. of the tangent line to the curve of f(x) = x^2 + 5x -5 at (0,-5).

Differentiate f(x) to obtain an expression for the derivative (slope of the tangent line):

             f '(x) = 2x + 5

Subst. 0 for x here:  f '(0) = 2(0) + 5 = 5     (at the point (0, -5))

Use the point-slope equation of a str. line to find the eqn of the tan. line:

y-k = m(x-h), where (h,k) is a point on the line and m is the slope:

y - [-5] = 5(x-0), or y+5 = 5x.  Then y = 5x - 5 is the eqn. of the TL to the given curve at (0,-5).
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Helppp i need answer now will give points
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Answer:

f(g(3)) = 3

Step-by-step explanation:

We are told to solve for f(g(3)). This is also saying f of g of 3.

To find f(g(3)), we need to plug 3 in for x in g(x), since it says g(3).

g(x) = 3(3) - 4

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Now, we plug that into f(x), because g(x) was placed inside f and replaces the x variable of f(x).

f(5) = 2(5) - 7

Solve.

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Answer:

x = 13sqrt(3) ft = 22.5 ft

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