Is #f(x)=(x-1)^2+2x^2-3x # increasing or decreasing at #x=-1 #?

Answer 1

Decreasing

To determine whether the function is growing or shrinking at x = -1

To find f'(x), differentiate and test its value at x = -1.

• The value of f(x) is increasing if f'(x) > 0.

• f(x) is decreasing if f'(x) < 0.

f(x) = # (x - 1 )^2 + 2x ^2 - 3x #

(multiply by brackets and gather similar terms)

f(x) # = x^2 - 2x + 1 + 2x^2 - 3x = 3x^2 - 5x + 1 #

Consequently, f'(x) = 6x - 5

and f'(-1 ) = - 11 < 0, indicating a decreasing f(x).

plot{3x^2 -5x+1 [-14.05, 14.05, -7.02, 7.03]}

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Answer 2

To determine if the function f(x) = (x - 1)^2 + 2x^2 - 3x is increasing or decreasing at x = -1, we can examine the sign of the derivative at that point. The derivative of f(x) is f'(x) = 2(x - 1) + 4x - 3. Evaluating this at x = -1 gives f'(-1) = 2(-1 - 1) + 4(-1) - 3 = -2 - 4 - 3 = -9, which is negative. Since the derivative is negative at x = -1, the function is decreasing at that point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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