Answer:
The directional derivate is given by:
Step-by-step explanation:
The directional derivative at point (x,y) is given by:
In which a is the x component of the unit vector and b is the y component of the unit vector.
Vector:
We are given the following vector:
Its modulus is given by:
The unit vector is given by each component divided by it's modulus. So
This means that
Partial derivatives:
So
Directional derivative:
The directional derivate is given by:
Answer:
The correct option is;
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
Which can be simplified as follows;
And further simplified as follows;
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
to increase m⁻¹(x) above the minimum.