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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:
1250 square feet
Step-by-step explanation:
If x is the length of the side perpendicular to the creek, then the third side is (100 -2x) = 2(50 -x). The area is the product of length and width:
A = x(2)(50-x)
We observe that this is a quadratic function with zeros at x=0 and x=50. The vertex (maximum) of a quadratic function is on the line of symmetry, halfway between the zeros. The value of x there is (0 +50)/2 = 25.
Then the maximum area is ...
A = (25)(2)(50 -25) = 1250 . . . . square feet
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<em>Additional comment</em>
Note that half the length of the fence is used in one direction (parallel to the creek), and half is used in the other direction (perpendicular to the creek). This 50/50 split is the generic solution to all sorts of rectangular corral problems, with or without a creek, with or without internal partitions.
Half the fence is perpendicular to the other half. (If the costs are different in different directions, then the cost is what is split 50/50.)
