find the area of a triangle if its two sides measure 6 inches and 9 inches and the bisector of the angle between the sides is 4
square root of 3
1 answer:
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The gradient of the tangent to the curve y = 5x³ + 3x² - x + 4 is 15x²+6x-1.
<h3>What is the gradient?</h3>A differential operator is used for a function having a vector value in three dimensions to produce a vector whose three components are the partial derivatives of the function with respect to its three variables.
The given equation for the curve is;
y = 5x³ + 3x² - x + 4
The gradient of the tangent to the curve is;
Hence,the gradient of the tangent to the curve y = 5x³ + 3x² - x + 4 is 15x²+6x-1.
To learn more about the gradient refer to;
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Answer:
a)
b)
Step-by-step explanation:
The first step to solve this question is finding the roots of the derivative of x.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that
, given by the following formulas:
In this question:
So
Finding the roots:
Simplifying by -3
So
Then
So the function can be divided in three intervals.
They are:
Less than -1
Between -1 and 5
Higher than 5
In which it increases and which it decreases?
Less than -1
Lets find the derivative in a point in this interval, for example, -2
Positive.
So in the interval of , the function increases.
Between -1 and 5
Will choose 0.
Negative.
So in the interval of , the function decreases.
Higher than 5
Will choose 6.
Positive
So in the interval of , the function increases.
(a) Find the interval on which f is increasing.
Using interval notation
b) Find the interval on which f is decreasing.