We know that the graph of g(x) is the result of a shift of 2 units down from f(x).
Then, f(x) and g(x) are related by:
Taking the derivative:
This is because the derivative of a constant number is 0. Finally, evaluating at x = 2:
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2 answers:
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The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.
<h3>What is a Function ?</h3>A function is a law that relates a dependent variable and an independent variable with each other
It is given that
y = 2tan (x - π/2) +3
To find the zeroes of a function that function has to be equated to zero.
2tan (x - π/2) +3 = 0
2tan (x - π/2) = -3
tan (x - π/2) = -3/2
x - 90 = -56.31
x = 33.69 degree
The zero of the function is at 33.69 degree
For finding the maxima /minima
the derivative is
dy/dx = 2 sec² (x - π/2)
the point at which the slope is zero is substituted in the second derivative to find maxima/minima
d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)
if the value is negative then it is a maxima and if it is positive it is a minima.
The vertical asymptote is found by finding the values that make the function undefined
x = 0+ πn
No horizontal or oblique asymptote
To know more about Function
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