Peter is x years old and his sister is 5 years older. If the product of their ages is 84, form an equation in x and solve it to
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Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.
<h3>What is the volume of a sphere?</h3>The volume of a sphere of radius r is given by:
Applying implicit differentiation, the rate of change is given by:
In this problem, we have that:
Hence the rate of change of the radius is given as follows:
The radius is increasing at a rate of 0.0081 cm per minute.
More can be learned about implicit differentiation at brainly.com/question/25608353
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Given:
The equation of the curve is:
To find:
The gradient (slope) of the given curve at point (2,7).
Solution:
We have,
Differentiate the given equation with respect to x.
Now we need to find the value of this derivative at (2,7).
Therefore, the gradient (slope) of the given curve at point (2,7) is 19.