Consider the function: 6x^2+5x-4 / 2x^2-7x-4 A) Identify the zeroes of the funct

Question

Consider the function: 6x^2+5x-4 / 2x^2-7x-4



A) Identify the zeroes of the function.

B) What (if any) are the vertical asymptotes? Write the equation(s) in proper form (ie., do not just give a number).

C) What (if any) are the horizontal asymptotes? Write the equation(s) in proper form.

D) first derivative:

E) second derivative:

F) Identify the intervals where the function is increasing and decreasing.

G) Find the equation of the line which is tangent to the curve at the point (0,1).

H) Find the equation of the line which is normal to the curve at the point (-3,1).

I) Find the critical points (extrema) for the function.

J) Find the point(s) of inflection. In your own words, what is the graphical significance of a point of inflection?

K) Plot your function in a reasonable interval, and include the asymptotic lines.

L) Plot the function including the lines found in parts G and H.

Explanation / Answer

Zeroes = 4/3

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