B) y = 3 = 2х Is this relation linear or non-linear? Explain why.
1 answer:
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Answer:
We have the function,
On simplifying, we get,
i.e.
Thus, the standard form of the function is .
Now, the factors of the given functions are (x+1) and (x+5).
<em>Since, the intercept form of the function is the factored form of the function.</em>
So, we have, intercept form of the function is .
Now, we know that,
Value of x-coordinate of the vertex is i.e.
i.e.
i.e. x= -3
Then, i.e.
i.e. f(-3)=-4
So, the vertex of the function is (-3,-4).
Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>
So, when x=0, we have, i.e. f(0) = 5
Thus, the y-intercept is (0,5)
Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>
Then, for f(x)=0, we have i.e.
i.e. x= -1 and x= -5
Thus, the x-intercept are (-1,0) and (-5,0).
a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
Evaluate the integral to solve for y :
Use the other known value, f(2) = 18, to solve for k :
Then the curve C has equation
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
The slope of the given tangent line is 1. Solve for a :
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
So, the point of contact between the tangent line and C is (-1, -3).