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find Dy/dt differentiate
Answers
Answer:
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Step-by-step explanation:
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Answer:
jaccording to Theorem 4 of Lesson 2.
The rate of change of f(x) is 2 for all values of x. f '(x) is constant. But that should be obvious. y = 2x − 5 is the equation of a straight line whose slope is 2. (Topic 9 of Precalculus.) And the value of the slope of a straight line is the rate of change of y with respect to x -- so many units of y for each unit of x.
There is no tangent to a straight line, because a tangent, by definition, touches a curve at one point only.
Example. The equation of a tangent to a curve.
a) Calculate the slope of the line that is tangent to y = x2 at the point
a) on the curve where x = 4.
b) What is the equation of that line?
Solution.
a) The slope of the tangent to the curve at x = 4 is the value of the
a) derivative at x = 4. The derivative of y = x2 is 2x. Therefore at
a) x = 4, the slope of the tangent is 8.
b) The equation of a straight line has this form:
y = ax + b,
where a is the slope of the line. Therefore, since a = 8, the equation is
y = 8x + b.
To find the value of b, we can now proceed as in Solution 1 to Problem 1 in Lesson 34 of Algebra. Since x = 4 in the function y = x2, then y = 16. The coördinate pair (4, 16) will solve that equation:
16 = 8· 4 + b
= 32 + b.
Therefore,
b = −16.