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You are given space that limit as h rightwards arrow 0 of fraction numerator g (3 + h) - g (3)/h = 7 and g (3) = 9. Find m and b so that the tangent space line of g (x) at x = 3, y = m x +b.

Respuesta :

Answer:

m = 7 and b = -12 therefore y = 7x - 12

Step-by-step explanation:

From the question we are given the first derivative of the function g to be 7, and it is known that the first derivative of a function is the slope, therefore the slope, m = 7.

Since we are looking for 'b' at x = 3 and we know that our slope is 7, we have:

g(3) = 7*3 + b. We are given g(3) = 9 so we have:

9 = 21 + b and b = -12.

Therefore, m = 7 and b = -12 and the equation of the line is y = 7x - 12.

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