Answer:
Step-by-step explanation:
We want to find the equation of the tangent line to the function:
At the point (-2, 6).
First, we will need the slope of the tangent line. So, differentiate* the function:
Find the slope when <em>x</em> = -2:
Now, we can use the point-slope form:
Our point is (-2, 6) and our slope is -11. Substitute:
Simplify:
Distribute:
And add six to both sides. Therefore, our equation is:
If you have not yet learned differentiation, here's the method using the difference quotient! The difference quotient is given by:
Here,<em> x</em> = -2. Substitute:
Substitute (we are given the point (-2, 6). So, f(-2) = 6).
Expand and simplify:
Distribute:
Simplify:
Evaluate the limit (using direct substitution):
Answer:
Step-by-step explanation:
To find the slope of the tangent at a point we will find the derivative of equation at that point.
a). y = x² - 10x
y' = 2x - 10
At (x = 2),
y' = 2(2) - 10
y' = 4 - 10
y' = -6
From the given equation,
y = 2² - 10
y = -6
Therefore, y-coordinate of the point is y = -6
Equation of the tangent at (2, -6) having slope = -6
y - 2 = -6(x - 2)
y - 2 = -6x + 12
y = -6x + 14
b). y =
At x =
y =
y =
y =
Now we have to find the equation of a tangent at
y' = 2x -
At x =
y' =
y' = 1 - 8
y' = -7
Therefore, equation of the tangent at will be,
y = -7x +
y = -7x +
Answer:
82.88%
Step-by-step explanation:
Given that:
Mean (μ) = 16.7 pounds
Standard deviation (σ) = 3.8 pounds
Number of pounds eaten = 11.5 = x
P(11.5 ≥ x ≤11.5)
P(x ≤ 11.5) :
Zscore = (x - μ) / σ
Zscore = (11.5 - 16.7) / 3.8
Zscore = - 5. 2 / 3.8
Zscore = −1.368421
P(Z ≤ - 1.3684) = 0.085593 (Z probability calculator)
P(x ≥ 11.5) ;
Zscore = (x - μ) / σ
Zscore = (11.5 - 16.7) / 3.8
Zscore = - 5. 2 / 3.8
Zscore = −1.368421
P(Z ≥ - 1.3684) = 0.91441 (Z probability calculator)
P(Z ≥ - 1.3684) - P(Z ≤ - 1.3684)
0.91441 - 0.085593 = 0.828817
0.828817 * 100% = 82.88%