Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
<h3>What is implicit differentiation?</h3>
Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
Since dx/dt=−2, we have that:
When y = π/4, x is given by:
xcos(y) = 2.
Hence:
Since cot(pi/4) = 1, we have that:
Which means that option a is correct.
More can be learned about implicit differentiation at brainly.com/question/25608353
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Answer:
2x + 1y =< 300
x + y =>150 units
y <= 2x
Step-by-step explanation:
Let x and y be the numbers of corndogs and shakes that will be sold.
<u>1.</u> The total cost of making these items is given by the sum of:
(x)(RM2) + (y)(RM1)
A total of RM300 is allocated for the cost of these items, so:
2x + 1y =< 300 [Units are RM)
<u>2.</u> Sales are expected to exceed 150 units, in total. This means:
x + y =>150 units
<u>3.</u> Sales for the shakes is less than 2 times that of the corndogs:
y <= 2x
The sine function has a minimum value of -1, so f(x) = 4sin( ) -1 will have a minimum value of -5.
g(x) obviously has a minimum value of -3.
h(x) has a squared term that cannot be negative, so its minimum value is +4.
f(x) has the smallest minimum value.
