a Find the value of \( a \). b Find the range of values of \( x \) for which the curve is a decreasing function. 6 The curve \( y=2 x^{3}+a x^{2}+b x-30 \) has a stationary point when \( x=3 \). The curve passes through the point \( (4,2) \). \( a \) Find the value of \( a \) and the value of \( b \). b Find the coordinates of the other stationary point on the curve and determine the nature of this point.
Added by Melissa H.
Close
Step 1
The curve is given by \( y = 2x^3 + ax^2 + bx - 30 \). The derivative is \( y' = 6x^2 + 2ax + b \). Show more…
Show all steps
Your feedback will help us improve your experience
Melissa Munoz and 54 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Audrey F.
The curve $y=a x^{3}+b x^{2}+c x+5$ touches $x$ -axis at $A(-2,0)$. The curve intersects the $y$ -axis at a point $B$ where its slope equals 3 . The value of $^{\prime} \mathrm{a}$ ' is (a) $-2$ (b) 2 (c) $\frac{-1}{2}$ (d) $\frac{1}{2}$
The line $y=a x+b$ is tangent to the graph of $y=x^{3}$ at the point $P=(-3,-27) .$ Find $a$ and $b.$
The Derivative
The Derivative and Limits
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD