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vodka [1.7K]
3 years ago
5

Let f(x)=x^3-x-1

Mathematics
1 answer:
alexira [117]3 years ago
6 0
f(x) = x^3 - x - 1

To find the gradient of the tangent, we must first differentiate the function.

f'(x) = \frac{d}{dx}(x^3 - x - 1) = 3x^2 - 1

The gradient at x = 0 is given by evaluating f'(0).

f'(0) = 3(0)^2 - 1 = -1

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.

The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

y = -x + c

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

f(0) = (0)^3 - (0) - 1 = -1

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:

y = -x + c \\\\ -1 = -(0) + c \\\\ -1 = c \\\\ \text{Equation of tangent is } \boxed{y = -x - 1}
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kari74 [83]

Answer:

The answer is "0.00001"

Step-by-step explanation:

Given value:

\to 3292.53429

when we round a hundred thousandths (100,000) value. So, the given rounding 3292.53429 to the nearest 0.00001.

7 0
2 years ago
If 15 litres of paint covers an area of 250 m2, what area (in m2) will 20 litres of paint cover?
Korvikt [17]

Answer: 333.33m²

Step-by-step explanation:

Since we are informed that 15 litres of paint covers an area of 250 m2, the the area that 1 liter of paint will cover will be:

= 250m²/15

= 16.666667m²

Therefore, the area that 20 litres of paint will cover will be:

= 16.666667m² × 20

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3 years ago
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Read 2 more answers
Solve |2x + 1| = 10
Ivan
By definition of absolute value we have two equalities:
 2x + 1 = 10
 2x + 1 = -10
 For 2x + 1 = 10:
 
2x + 1 = 10
 2x = 10-1
 2x = 9
 x = 9/2
 For 2x + 1 = -10:
 
2x + 1 = -10
 2x = -10-1
 2x = -11
 x = -11 / 2
 Answer:
 
{-11/2, 9/2}
3 0
3 years ago
Simplify to create an equivalent expression. \qquad{2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)
maw [93]

Answer:

  54y² +255y +300

Step-by-step explanation:

Such an expression is simplified by eliminating parentheses and combining like terms.

<h3>Eliminate parentheses</h3>

Taking the given expression at face value, we have ...

  {2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)

  = {6y +12 +12 +3y}(6y +12) +12 +3y

  = (9y +24)(6y +12) +12 +3y

  = (9y)(6y +12) +24(6y +12) +12 +3y

  = 54y² +108y +144y +288 +12 +3y

<h3>Combine like terms</h3>

  = 54y² +(108 +144 +3)y +(288 +12)

  = 54y² +255y +300

8 0
2 years ago
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